Superphysics
Chapter 4b

# Going Beyond the Natural Capacity

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As output increases, a firm’s additional labour will add less productivity relative to the hourly-common-wage paid to it.

We subsume the non-homogeneity of equally paid work in the equipment. We regard it as less and less adapted to employ the available labour units as output increases. This is the opposite of regarding the available labour as less and less adapted to use a homogeneous capital equipment.

Thus, if all specialised are already utilized and common labour adds to a higher labour cost per unit of output, then the rate of return from the equipment becomes smaller faster as employment increases. [6]

Thus, our assumption of a homogeneous unit of labour is only problematic if there is great instability in the relative pay of different hourly-common-labour. This can be solved by supposing a rapid liability to change in the supply of labour and the shape of the aggregate supply function.

Much unnecessary perplexity can be avoided if we limit ourselves strictly to the two units= hourly-common-wage and hourly-common-labour, when we are dealing with the behaviour of the economic system as a whole.

We only use units of particular outputs and equipment when we are analysing the output of individual firms or industries in isolation.

The vague concepts are:

• the quantity of output as a whole
• the quantity of capital equipment as a whole
• the general price levels

We can use these when we are comparing historical data.

We shall measure the changes in current output as:

• the number of men employed on the existing capital equipment
• skilled workers being weighted according to the ordinary pay

We do not need a quantitative comparison between this output and the output from associating a different set of workers with a different capital equipment.

To predict how entrepreneurs will respond to a shift in the aggregate demand function, we do not need to know how the quantity of output* compares to:

• the standard of life
• the general level of prices

*Superhysics note: This is actually why we created the grain index

The aggregate supply function, through the hourly-common-wage and hourly-common-labour, can handle the:

• conditions of supply
• elasticity of supply relating output to price

This does not need any reference to quantities of output, whether individually or as a whole.

The aggregate supply function for a firm (and an industry as a whole) is:

``````Zr = φr(Nr)
``````
• Nr is the target level of employment
• Zr is the return expected that will then induce Nr

If employment Nr causes an output Or, where Or = ψr(Nr), it follows that p = Zr/Or = φr(Nr)/ψr(Nr) is the ordinary supply curve.

Thus, in the case of each homogeneous commodity, for which Or = ψr(Nr) has a definite meaning, we can evaluate Zr = ψr(Nr) in the ordinary way/

But we can then aggregate the Nr’s in a way which we cannot aggregate the Or’s, since ΣOr is not a numerical quantity.

Moreover, if a given aggregate employment will be distributed in a unique way between different industries, so that Nr is a function of N, further simplifications are possible.

## Author’s Footnotes

1. If X stands for any quantity measured in terms of money, it will often be convenient to write Xw for the same quantity measured in terms of the wage-unit.

2. This is why the supply price of output rises with increasing demand even when there is still a surplus of equipment identical in type with the equipment in use.

If we suppose that the surplus supply of labour forms a pool equally available to all entrepreneurs and that labour employed for a given purpose is rewarded, in part at least, per unit of effort and not with strict regard to its efficiency in its actual particular employment (which is in most cases the realistic assumption to make), the diminishing efficiency of the labour employed is an outstanding example of rising supply price with increasing output, not due to internal diseconomies.

1. I cannot say how the supply curve ordinarily is supposed to deal with the above difficulty. Those who use this curve have not made their assumptions very clear. Probably they unrealistically assume that labour is always rewarded with strict regard to its efficiency for that purpose.

The varying efficiency of labour is due to equipment because the increasing surpluses, which emerge as output is increased, accrue in practice mainly to the owners of the equipment and not to the more efficient workers (though these may get an advantage through being employed more regularly and by receiving earlier promotion);

Men of differing efficiency working at the same job are seldom paid at rates closely proportional to their efficiencies. Where, however, increased pay for higher efficiency occurs, and in so far as it occurs, my method takes account of it; since in calculating the number of labour units employed, the individual workers are weighted in proportion to their remuneration.

On my assumptions, complications arise where we are dealing with particular supply curves, since their shape will depend on the demand for suitable labour in other directions. It would be unrealistic to ignore these complications.

But we need not consider them when we are dealing with employment as a whole, provided we assume that a given volume of effective demand has a particular distribution of this demand between different products uniquely associated with it.

It may be, however, that this would not hold good irrespective of the particular cause of the change in demand. E.g. an increase in effective demand due to an increased propensity to consume might find itself faced by a different aggregate supply function from that which would face an equal increase in demand due to an increased inducement to invest. All this, however, belongs to the detailed analysis of the general ideas here set forth, which it is no part of my immediate purpose to pursue.